Chapter 12 - Section 12.5 - Tangential and Normal Components of Acceleration - Exercises - Page 669: 6

$a=2 \ T +\sqrt 2 \ N$

$v(t)=\dfrac{dr}{dt}= e^t (\cos t -\sin t)i+e^t(\sin t+ \cos t ) j+\sqrt 2 \ e^t k $ or, $|v(t)|=e^t \sqrt {(\cos t -\sin t)^2+(\sin t+\cos t)^2+2} \\= e^t \sqrt {1+1+2} \\=e^t\sqrt {4}=2e^t$ Now, $a(t)=\dfrac{d \ v(t)}{dt}= 2e^t$ or, $|a(0)|= 2e^{0}=2$ $a_{N}=\sqrt {|a|^2 -a^2_{T}}=\sqrt {(\sqrt 6)^2 -(2)^2}==\sqrt {6-4}=\sqrt 2 $ and $a=a_T T+a_{N}=2 \ T +\sqrt 2 \ N$